Question

hiiiiiiiii......allllll!!!!!!
plzzzz tell someone,whats the rules of series solution?????:::::\\\\\\\\

Answer 1

Series solution as in, a series solution to a linear ordinary differential equation, or something else...

Answer 2

is this for an introductory differential equations class?

Answer 3

its not linear...its higher order differential eqn.....

Answer 4

nooo......richywwww

Answer 5

haha then I can't help you. sorry!

Answer 6

:::''''''((((((

Answer 7

hlwwww???????can none of u help me frnd??????:::::\\\\\\\\

Answer 8

@tonmoy24 A linear differential equation can be a higher order differential equation. I think you're getting "linear" confused with "lower-order", or possibly you are confusing "higher-order" for "non-linear". If you are confused in the first sense, then I can help.

Given\[...+p_3(x)y'''+p_2(x)y''+p_1(x)y'+p_0(x)y=0\]A series solution of the form\[y=\sum_{n=0}^{\infty}a_n (x-x_0)^n\]exists if \[\frac{p_i(x)}{p_{i+1}(x)}\]is analytic around x0. That is to say, the above function has a Taylor series that converges in an open interval containing x0. Whew!

Answer 9

(For all i). Sorry.

Answer 10

*all applicable i

Answer 11

sorrrrrryyyyy dear!!!!!u dnt get the ques.......its a differential equation which is mixed up with lower nd higher order...now solve it with series method......

Answer 12

@tonmoy24 I gave you the most general conditions for the problem you specified...

Answer 13

@tonmoy24 You can't have a differential equation that's "a mixed up with higher and lower order differential equation". If you have third derivatives or greater, it's automatically a higher order differential equation. I gave you the conditions for the existence of a series solution to such an equation (that is also linear). The actual finding of a solution is even easier, in my opinion. Here, look at this link. I'm tired of saying stuff:
http://www.sosmath.com/diffeq/series/series01/series01.html
It's basically the same for higher-order

Answer 14

hmmmmm....thnx dear:::::))))get it!!!!!!!